{"id": "c46", "title": "C46 — The added families expose one already retained endpoint match", "filename": "490d_C46_Mirror_Report_20260922.md", "role": "Research action", "step": 46, "sha256": "29eb86b1c4b59fa4ca9b2632d995f4be3938043fb9b66e7593c726ece26a1f6b", "bytes": 2720, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_30_step_campaign_20260922/C46/490d_C46_Mirror_Report_20260922.md"], "download": "/sources/29eb86b1c4b59fa4ca9b2632d995f4be3938043fb9b66e7593c726ece26a1f6b.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Rounded", "Mirror / 529"], "excerpt": "C46 — The added families expose one already retained endpoint match\n\n22 September 2026 · Step 24 of the authorized 30-step Mirror continuation (C23–C52).\n\nRelease the selected-length match by writing\n\n\\\nm=\\ell_\\rm cumulative-\\ell_\\rm regular,\\qquad\nu=c-(2K+m),\\qquad B=17K+\\rho.\n\\\n\nRetain the old partition assignments A", "content": "# C46 — The added families expose one already retained endpoint match\n\n22 September 2026 · Step 24 of the authorized 30-step Mirror continuation (C23–C52).\n\nRelease the selected-length match by writing\n\n\\[\nm=\\ell_{\\rm cumulative}-\\ell_{\\rm regular},\\qquad\nu=c-(2K+m),\\qquad B=17K+\\rho.\n\\]\n\nRetain the old partition assignments A=−s−3K, Z=−s+7K and H=A−2K, and define U=−u. Exact subtraction gives:\n\n| Paths | Residual from their labelled multiple |\n| --- | --- |\n| old 17; new 15 intersection; old 20 and old 22 | ρ |\n| new u→v 17; u→s 19; right 12 and 22; joined 24 | ρ+m |\n\nThe source has m=0: the cumulative c−cm length and the selected regular comparison are both 598. This is the C20/C12 retained match, now visible in the extended paths. With that match held, every new right-side residual is simply ρ, so the additions provide no new scalar calibration beyond the existing 17-fold closure.\n\nIf m is independently released, an old 17-fold residual and a new 19-fold residual have rank two in (ρ,m). Their difference measures m. That is a useful conditional diagnostic, not evidence that the original source values were independently predicted twice.\n\nThe reduced C22 constraints still supply ρ=2ω−C/2. The new graph therefore preserves the distinction between primitive source balances, the regular/cumulative endpoint binding, and dependent family widths.\n\n**Validation.** 4 exact arithmetic/structural checks passed. The ten frozen dependencies passed hash verification; all three generated outputs replayed byte for byte in isolation, and the original dependencies remained unchanged. This step reads completed certificates and does not execute their campaigns.\n\n**Scope and provenance.** Controlling File_18 and File_09 remain unchanged. Regular Gears apply only to Noah/Shem/Flood; SP person companions only to Noah/Shem. Creation and Conquest fields remain fixed. Native LXX ON, explicitly derived OFF, independent Flood start/close, and paired suffix inversion at January AD 1 remain in force. No civil year zero, upstream Gear transport, primers, Rounded campaign, or localized −33 is introduced. These are new continuation reports, not recovered historical Reports 11–25. Evidence is conditional on the supplied project model, not a proof of literary intention or independent historical dating.\n\n**Source locators.** File_09 §3.1 (paired Mirror); File_18 §§2.1.3, 3.1–3.2, 6B and 6D (qualified regular and cumulative fields); frozen C15 typed graph, C16 domain certificate, and C22 reduced scale/constraint certificates.\n\n**Best next bounded step — High sufficient.** Build a bounded residual diagnosis that distinguishes width errors from endpoint-binding errors.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}